Two Rotating Disks Contacting Along Edge

1. The problem statement, all variables and given/known data
Two disks, rotating in the opposite direction of the other, are held together on their rotating ends, acting as toothless gears. The bottom disk is slightly skewed in one direction, and therefore causes a frictional force on the top disk, and thus an equal and opposite force on itself. Show the direction and magnitude of these forces.2. Relevant equations
Basic Physics equations: Newtons Laws of motion, Friction Force equation, etc.3. The attempt at a solution
I first listed the number of known variables that could affect the situation.
Dimensions of the disks, angular velocities and directions, and friction coefficient.
I drew a sketch of the problem and drew in the angular velocities and forces (sorry for terrible paint skills)
Red: Angular Velocities Brown: Forces holding two together Green: Contact Point
The forces on each disk will be in the opposite direction of the angular velocities on each.
I'm stuck on how to convert the angular velocities into an acting force at the point of contact. I also assume that the point of contact is basically a single point, as skewing the disks in one direction would cause the contact surface to reduce from a line to (basically) a single point. I understand that the two disks are moving in a different direction at that contact point, but I don't quite know how to quantify this using the assumed variables. More looking for hints as to how to find this.

the contact surface to reduce from a line to (basically) a single point

You may find it more fruitful to leave the contact area as a small patch, effectively flat. Take one of them to be the driving surface, moving at a given speed in a given direction. The other one is free to move at a certain angle to that direction only (i.e. ignore any load inhibiting its rotation on its axis).
Can you think of a criterion which will determine the rate of that movement? Remember that friction opposes relative motion of the surfaces in contact.